(Doubling your money!) Consider the recurrence relation for compound interest x(0) = P; x(n) (1+i)x(n-1) for n 1. a. For interest rates, i, between 2.5% and 25% in increments of 0.5%, find the number N = N(i) of time periods necessary for the principal P to double (choose P to be $1000). Graph N(i) vs. i for these interest rates. Note: For plotting the graph of N(i), enter i-values as percents, not decimals, i.e. i = 2.5, 3, 3.5, ..., 25. b. Also graph the function D(i) = 72/i vs. i for the same values of i chosen above. Note: For calculating D(i) as well as plotting the graph of D(i), enter i- values as percents, not decimals, i.e. i 2.5, 3, 3.5, ..., 25. c. For what values of i chosen above is the relative error between N(i) and D(i) less than two percent in absolute value. For the relative error calculations, consider N(i) to be the actual value and D(i) to be the estimate. (Recall we saw the idea of relative error in Lab 1.) d. What can you conclude about the doubling time for a principal P earning compound interest at a rate % per period?